On-demand anchoring of wireless soft miniature robots on soft surfaces

Significance Anchoring soft millirobots on surfaces, such as biological tissues, is essential to perform long-duration medical functions robustly on a target position. For robust anchoring, we propose a wireless mechanism that can be precisely controlled by remote heating to achieve on-demand needle release and mechanical interlocking. Such a mechanism can be easily integrated on existing untethered soft robots, allowing them to anchor robustly to soft surfaces while retaining their locomotion capabilities. Furthermore, we demonstrate advanced functionalities of such robots, such as controlled surface detachment and subsurface drug delivery into three-dimensional cancer spheroids. Given these capabilities, the proposed mechanism can serve as a platform for the development of soft robots with a new suite of biomedical capabilities.


Analysis of the mechanism
Based on high-speed images of the trigger event (Fig. S3A), the puncturing process was divided into six phases: initial, deflection, puncture, needle insertion, recoil and final phase (Fig. S3B). We modelled the mechanism as a spring-mass system, with the soft surface and spring being modelled as serial springs (Fig. S3C). As the time taken for anchoring is less than a second (Fig. 1E), the response of the surface is dominantly elastic and can be characterized by a linear stress-strain response (i.e., spring) (1). In the initial phase (phase I), the mechanism is oriented towards the surface and there are no net forces acting on the soft surface or the needle. We set the origin to be at the soft surface and define 1 as the maximum surface deflection. 1 need not always be at the needle tip as seen in the illustrations of the later stages (phases IV and V). In the deflection phase (phase II), the mechanism is triggered and the spring drives the needle into the surface by 1 . There is no cutting or penetration of the surface in this phase. When 1 reaches a value such that the corresponding stress intensity factor that accompanies the stress field induced at the needle tip exceeds the fracture toughness of the surface, the needle penetrates the surface (phase III). The displacement at this point is recorded as . Frictional force will start to act from this phase onwards. Since friction acts along the length of the needle, we assume that the pressure acting along the length of the needle is constant and is proportional to the depth of insertion 1 − . This process continues until the copper plate driving the needle impacts the surface or until the needle stops if the needle is sufficiently long. At this point (phase IV), deflection of the surface is maximum and the velocity of 1 , which corresponds to the mass of the copper plate, is zero. After this point, the spring loses contact with 1 and the surface starts releasing the stored elastic energy. This accelerates 1 in the opposite direction until all the energy is released (phase V). In all these phases, since the casing is not fixed and is free to move, the casing accelerates in the opposite direction.
By examining the equations of motion of each phase (next section), a system of ordinary differential equations describing the motion of the head and the casing during the process was obtained.
Equations corresponding to the deflection phase (phase I to phase II) were then numerically solved in MATLAB using the ode45 solver. The stiffness of the soft surfaces were computed from the experimentally determined Young's modulus based on a previously proposed method (2). These surfaces were selected to cover the stiffness of living tissues in the kPa range, which encompasses most organs inside the human body (3). For the spring constants, we directly used the values provided by the manufacturer for the springs. To increase the accuracy of the model, parameters used in the simulations were experimentally determined. All other simulation parameters are provided in Table S2. In the simulations, we only considered the case where a barbless needle, placed right next to the surface, enters the surface at 90°. When the angle of insertion or distance from the surface changes, this results in a reduction in the force supplied to deform the substrate.
Similarly, the effect of the barb can be reflected in this model by introducing a penalty term.
Specifically, addition of a barb will increase the apparent bevel angle of the needle and reduce the force applied (2). As these affect all configurations equally and are not specific to a particular configuration, the same trends will hold and we do not consider their effects in the model.

Equations of motion for the various stages
Between 1 and 2: [ ℎ ℎ ℎ

Initial biocompatibility studies
To demonstrate the biocompatibility of long-term anchoring on tissue surfaces, we cultured the needles with a human fibroblast cell line. We seeded the fibroblast cells on top of the needles, and observed their viability after 72 hours of culture. The fibroblasts demonstrated clear viability in the culture environment and at the interface of the needle while having spindle-shaped, healthy morphology (Fig. S11A). The confocal microscopy analysis also revealed the 3D migration of fibroblasts towards the needle surface after 72 hours, demonstrating the biocompatibility of the needle interface (Fig. S11B, C). To demonstrate that the needles and the by-products released during degradation were non-toxic (Fig. S11D), the base material of the needle was grounded into powder and cultured with the fibroblasts at different concentrations. The cell viability analysis showed that the by-products of degradation (up to the concentration of 600 / ) did not cause any adverse effect on the cells after 72 hours, demonstrating the versatility and compatibility of the material (Fig. S11E).